(Common for both Red Hat and Slackware distributions.)
Before starting, make sure that you have access to the ZIP drive;
either by having ppa in the kernel or by having the ppa module
loaded. One easy way to find this out is by checking dmesg:

==> dmesg

You may have to pipe this to more as dmesg tends to be rather long.
Here's a snip from mine:

Again, be sure not to include ppa as a module, but rather in the
kernel. Thus far, without the use of the parport kernel patch
(see 1.4), the ppa driver will not allow the passive port of the ZIP
drive to be used for a printer, so you may want to say no to parallel
printer support:

Parallel printer support (CONFIG_PRINTER) [N/y/m/?]

NOTE: For more information concerning the ppa driver, please
refer to the ZIP-Drive mini-HOWTO.

Once the kernel is configured, make the kernel:

==> make dep; make clean; make zImage

The new kernel should be found in arch/i386/boot/zImage.

Getting the kernel to a floppy

After having to have 4 separate floppies due to different kernels
and needing different parameters, (plus the great email I got
telling me how to do this) I have included a section on LILO as one
of the means of creating a bootable floppy.

LILO installation

For those who have to, or for that matter just want to, have several
kernels on one floppy (now adays, mine are too large) or just want
to be able to pass arguments (such as single user mode) I received
email on how to install LILO on a floppy.

Creating the ext2 filesystem

To create an ext2 filesystem on a floppy, just do the same command
for the ZIP disk:

==> mke2fs -t /dev/fd0

Copying the essential files

Next, make sure there's a directory for a mount point, and mount the
floppy (I used /mnt/floppy):

==> mount /dev/fd0 /mnt/floppy -t ext2

is to boot properly, you'll need the same files that LILO uses on your
current Linux installation.

NOTE: The file locations here are from my machine
and may not be the same for everyone.

==> cp /boot/boot.b /mnt/floppy

==> cp /boot/map /mnt/floppy

==> cp /usr/src/linux/arch/i386/boot/zImage /mnt/floppy/vmlinuzDESK

Now to create the config file for LILO, now I miss the liloconfig
program... (Thanks to Javier Rodriguez for this info) First, create
the LILO config file, /mnt/floppy/lilo.conf, for the kernel(s) for
the ZIP disk. Here's what I used so that I could have different
kernels to test with: